Question: Express your answer as a mixed number simplified to lowest terms. $11\dfrac{1}{10}-9\dfrac{4}{6} = {?}$
Solution: Simplify each fraction. $= {11\dfrac{1}{10}} - {9\dfrac{2}{3}}$ Find a common denominator for the fractions: $= {11\dfrac{3}{30}}-{9\dfrac{20}{30}}$ Convert ${11\dfrac{3}{30}}$ to ${10 + \dfrac{30}{30} + \dfrac{3}{30}}$ So the problem becomes: ${10\dfrac{33}{30}}-{9\dfrac{20}{30}}$ Separate the whole numbers from the fractional parts: $= {10} + {\dfrac{33}{30}} - {9} - {\dfrac{20}{30}}$ Bring the whole numbers together and the fractions together: $= {10} - {9} + {\dfrac{33}{30}} - {\dfrac{20}{30}}$ Subtract the whole numbers: $=1 + {\dfrac{33}{30}} - {\dfrac{20}{30}}$ Subtract the fractions: $= 1+\dfrac{13}{30}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{13}{30}$